Method for fusing multiple gps measurement types into a weighted least squares solution

ABSTRACT

A method of calculating position data for an airborne aircraft using a GPS-based airborne navigation system includes the processing of a position component of a relative state function by fusing a plurality of different types of measurement data available in the GPS-based system into a weighted least squares algorithm to determine an appropriate covariance matrix for the plurality of different types of measurement data.

CROSS-REFERENCE TO RELATED APPLICATION

This applications claims the benefit under 35 U.S.C. Section 119(e), ofco-pending Provisional Application No. 60/822,195, filed Aug. 11, 1006,the disclosure of which is incorporated herein by reference in itsentirety.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

BACKGROUND

1. Field of the Invention

The present invention relates to Global Positioning System (GPS)-basedRelative Navigation Systems, and more particularly to a method forprocessing the relative state of the position component of an airbornenavigation system.

2. Background of the Invention

A need has been found for providing a rapidly deployable, adverseweather, adverse terrain, day-night, survivable, and mobile precisionapproach and landing capability that supports the principles of forwardpresence, crisis response and mobility. The capability should enablemilitary forces to land on any suitable surface world wide (land andsea), under both peace time and hostile conditions, with ceiling and/orvisibility the limiting factor.

The Joint Precision Approach and Landing System (JPALS) is an integralpart of such a strategic system. JPALS is a differential GPS thatprovides a rapidly deployable, mobile, adverse weather, adverse terrain,day-night, and survivable precision approach and landing capability. TheJPALS allows an aircraft to land on any suitable land or sea-basedsurface worldwide, while minimizing the impact to airfield operations,because of low ceiling or poor visibility. This approach and landingsystem provides the capability of performing conventional and specialoperations from a fixed-base, shipboard, and austere environments undera wide range of meteorological and terrain conditions.

One of the primary functions of sea-based JPALS is to determine therelative state (position, velocity and acceleration) of an airbornevehicle with respect to its assigned ship. This function is called“Relative State Function” or “Relative Navigation” (“RelNav”). Existingcivil and military systems do not satisfy JPALS requirements becausethey have a number of shortcomings that limit joint operations. Themultiplicity of systems, in and of itself, hinders inter-Service, civil,and allied operations.

Among the limitations of conventional systems, especially as applied tocalculating position data of an aircraft closing in on a target, is thatin order to calculate an aircraft's position, numerous measurements musttaken. Certain measurement types have better accuracy but require moreprocessing time to achieve results. Traditionally, four measurements ofthe same type are needed to be used in a solution; otherwise optimalsolutions can not be made available. Conventional methods that use aweighted least squares position solution use only a single measurementtype. Furthermore, conventional methods have been less than satisfactorywhen relative position estimation is needed between two moving vehicles(e.g., between an aircraft and a ship).

SUMMARY OF THE INVENTION

As used herein, the terms “invention” and “present invention” are to beunderstood as encompassing the invention described herein in its variousembodiments and aspects, as well as any equivalents that may suggestthemselves to those skilled in the pertinent arts.

The present invention provides a novel and effective system and methodfor a GPS-based airborne navigation system to process the positioncomponent of the Relative State Function by fusing different typesmeasurement data, i.e., data representing several different measuredparameters. More specifically, the present invention provides animproved method of calculating the position data of aircraft closing inon target locations.

The present invention enhances the speed and accuracy of such positioncalculations. This is accomplished by the fusing some or all of thedifferent types of measurement data available in a GPS-based system intoa weighted least squares algorithm to determine the appropriatecovariance matrix, given the different measurement types. This methodallows optimal accuracy in the position solution by including allsatellites, and their best available measurements. Moreover, theinvention can operate and provide satisfactory results whenever relativeposition estimation is needed between two vehicles (e.g., an aircraftand a ship).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of the overall set up of a relative navigationsystem, of the type in which the system and method of the presentinvention may be employed;

FIG. 2 is an architectural block diagram of an airborne relative statesystem that includes an airborne RelNav computer system and interfaces;

FIG. 3 is a flow diagram showing major functional/processing blocks ofan airborne RelNav system including the RelNav computer system andinterfaces; and

FIG. 4 is a flow chart identifying process steps to calculate positiondata in accordance with present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following definitions are provided as they are typically (but notexclusively) used in GPS-based navigation systems implementing thevarious adaptive aspects of the present invention.

The GPS is a satellite-based navigation system having a constellation of24 Earth orbiting satellites. These satellites are approximatelyuniformly dispersed around six circular orbits having four satellites ineach orbit. Each GPS satellite transmits at two frequencies: L1 (1575.42MHz) and L2 (1227.60 MHz). The L1 frequency has two differentspread-spectrum codes modulated on it: a coarse acquisition (CA) code,and a Y code. The Y code is also modulated onto the L2 carrier.

Earth centered, Earth fixed (ECEF) is a Cartesian coordinate system usedfor GPS. It represents positions as X. Y. and Z coordinates in meters.The point (0.0.0) denotes the center of the earth, hence the nameEarth-Centered.

World Geodetic System of 1984 (WGS 84) a geodetic reference systems usedby GPS and developed by the U.S. Defense Mapping Agency.

Double Difference (technique) is a measurement method using tworeceivers. Differences are formed at each measurement epoch between twosatellites on each receiver and then between the same two receivers.

To better understand the invention, an overall system description isgiven, and the function and operation of the present invention will bedescribed in specific detail.

FIG. 1 shows an overall set up for a relative navigation system 100between an aircraft 102 and a ship 106. Both the aircraft 102 and theship 106 receive L1 and L2 GPS measurements from a GPS satelliteconstellation 104. The ship 106 processes its measurement data togenerate its state (position, velocity) and estimated wide lane phaseambiguities. Ship measurement data are generated from as many as 4 GPSantennas. The computed ship state (position, velocity) and estimatedwide lane phase ambiguities are broadcast, using radio frequencies, foruse by all aircraft within broadcast range of the ship.

The aircraft 102 combines its own measurements with the shipmeasurements, state, and ambiguities received over the broadcast, toproduce a relative vector solution between its own GPS antenna and theship's reference point. It also determines the quality of the relativevector solution.

Referring to FIG. 2, an Airborne Relative State System 110 includes anAirborne RelNav computer system 116 that computes the relative positionand velocity vector between the ship 106 and the aircraft 102. It alsocomputes the uncertainty of the computed position and velocity vectors.The computed relative state and its uncertainty are inputted to aguidance and control (G&C) system 118 for guidance and control of theaircraft 102.

To assure system modularity, the interfaces in the airborne relativestate system 110 are well defined. Five such interfaces are shown inFIGS. 2 and 3:

Aircraft Avionic System 117 and its associated avionics interface (AI)117A;

Airborne GPS receiver 119 and its associated GPS receiver interface(AGRI) 119A;

Airborne Data Link 112 and its associated data link interface (DLI)112A;

Configuration data 114 and its associated configuration date interface(CDI) 114A; and

Airborne Guidance and Control system 118 and its associated guidance andcontrol interface (GCI) 118A.

The Relative State Function has been partitioned into severalsub-functions, as illustrated in FIG. 3. The algorithms to implementeach sub-function are not described; only the sub-functions performedare identified. A detailed description of functionality and algorithmiicimplementation is provided only for the Precision Relative State module(PRS) 137, since its architecture and operation embody the presentinvention.

The functional representation of the RelNav computer system 116 in FIG.3 identifies nine functional blocks along with three sub-blocks. AMeasurement Management and Validation (MMV) function 129 receives datafrom Airborne GPS receivers 119 via the AGRI 119A, Configuration Data114 via the CDI 114A, and Ship Data Uncompressed (DU) 125 via the DLI112A. The DU 125 converts ship position and velocity data to WGS-84 ECEFcoordinates. The MMV function 129 validates Pseudo Range (PR) andCarrier Phase (CP) data (“Measurement Validation” 127), synchronizes theuse of ephemeral data between ship and aircraft (“Sync. of EphemeralData” 127 a), propagates ship position and velocity data to aircrafttime (“Propagation of Ship Data . . . ” 126), synchronizes aircraftmeasurements to ship time (“Sync. of Aircraft Data . . . ” 128), andcomputes the sigma value of each aircraft GPS measurement (“ComputeSigma” 128 a).

A Ship Troposphere Correction (STC) function 131 applies troposphericcorrections to ship GPS measurements. An Aircraft Troposphere Correctionfunction (ATC) 132 applies tropospheric corrections to aircraft GPSmeasurements. An Absolute Position and Velocity (APV) function 130computes the aircraft s absolute position, the positions of satellitesfrom the ephemeral data, and the aircraft's absolute velocity solution.A Relative Measurements (PM) function 133 calculates Double-Difference(DD) measurements (L1 PR, L2 PR, L1 CP, L2 CP. WL CP, NL PR) at shiptime, and calculates variance components (multipath and noise,ionosphere corrections, troposphere corrections) of DD measurements fromSingle-Difference (SD) measurements (L1 PR, L2 PR, L1 CP, L2 CP, WL CP,NL PR) and variances at ship time. The satellite highest in elevation ischosen as a reference, and the PM function 133 calculates covariancematrices components (multipath and noise, ionosphere corrections,troposphere corrections) of the DD measurements. Since ship measurementsmay come from four separate antennas, four separate solutions may berequired.

A Wide Lane Ambiguities (WLA) function 134 determines WL floatambiguities and covariance (Ship UD, Aircraft UD, SD, and DD). Itdetermines the probability of correctly fixing WL ambiguities, and italso determines the Discrimination Ratio of integer ambiguities,validates integer ambiguities, and fixes WL ambiguities. An L1/L2Ambiguities (L1L2A) function 135 is performed assuming WL fixedambiguities have been resolved successfully. It determines L1 and L2float ambiguities and covariance, determines the probability ofcorrectly fixing L1 and L2 ambiguities, determines the DiscriminationRatio (DR) of resolved L1 and L2 integer ambiguities, validates integerambiguities, and fixes L1 and L2 ambiguities. A Basic Relative State(BRS) function 136 computes a Basic Relative State (position andvelocity) at aircraft time and computes a Covariance of Basic RelativeState (position and velocity).

The G & C Interface (GCI) 118A provides precision relative state outputsto Guidance and Control functions, and it receives input from thePrecision Relative State module (PRS) 137. The Avionics Interface (AI)117A provides Basic Relative State outputs to the aircraft avionicssystem. The PRS module 137 determines a Precision Relative State only ifan aircraft's distance to the ship is less than 10 nautical miles Asatellite should only be considered in a particular solution if itsmeasurements have been consecutively available for a configurable amountof time. The initial interval is set at 30 seconds or 60 samples.

A functional block diagram for the Precision Relative State (PRS) module137 is shown in FIG. 4, illustrating the different calculationsperformed to arrive at a Precision Relative State solution. A firstcomputing module 138 computes code range and phase range values fromMeasurements and Covariance. DD NL Code Range Observables are calculatedby Equations (1), (2) and (3):

$\begin{matrix}{\lambda_{n\; 1} = \frac{\lambda_{1}\lambda_{2}}{\lambda_{2} + \lambda_{1}}} & (1) \\{R_{nl} = {\lambda_{n\; 1}\left\lbrack {\frac{R_{1}}{\lambda_{1}} + \frac{R_{2}}{\lambda_{2}}} \right\rbrack}} & (2) \\\begin{matrix}{C_{R_{nl}} = {{\left( \frac{\lambda_{n\; 1}}{\lambda_{1}} \right)^{2}C_{{{DD\_ L}_{1}{\_ M}},E}} +}} \\{{{\left( \frac{\lambda_{n\; 1}}{\lambda_{1}} \right)^{2}C_{{{DD\_ L}_{2}{\_ M}},E}} + C_{{DD\_ L}_{1}{\_ tropo}} +}} \\{{\left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{2}C_{{DD\_ L}_{1}{\_ iono}}}}\end{matrix} & (3)\end{matrix}$

where R₁ and R₂ are DD code ranges

DD Phase Range Observables are calculated by Equations (4) to (9): L1Float:—

Φ₁ _(≦) _(flo)=Φ₁−λ₁ N ₁ _(—) _(flo)   (4)

C _(Φ) ₁ =C _(DD) _(—) _(L) _(1—) _(m,e) +C _(DD) _(—) _(L) _(1—)_(iono) +C _(DD) _(—) _(L) _(1—) _(tropo)

C _(Φ) _(1 flo) =C _(Φ) ₁ +λ₁ ² C _(N) _(1—) _(flo)

L2 Float:—

Φ₂ _(—) _(flo)=Φ₂−λ₂ N ₂ _(—) _(flo)

C ₁₀₁ ₁ =C _(DD) _(≦) _(L) _(2—) _(m,e) +C _(DD) _(—) _(L) _(2—) _(iono)+C _(DD) _(—) _(L) _(2—) _(tropo)   (5)

C _(Φ) _(2—) _(flo) =C _(Φ) ₂ +λ₂ ² C _(N) _(2—) _(flo)

L1 Fixed:—

Φ₁ _(—) _(fix)=Φ₁−λ₁ N ₁ _(—) _(fix)   (6)

C_(Φ) _(1—) _(fix) =C_(Φ) ₁

L2 Fixed:—

Φ₂ _(—) _(fix)=Φ₂−λ₂ N ₂ _(—) _(fix)   (7)

C_(Φ) _(2—) _(fix) =C_(Φ) ₂

$\begin{matrix}{{{WL}\mspace{14mu} {Float}\text{:}\text{-}}{\lambda_{w\; 1} = \frac{\lambda_{1}\lambda_{2}}{\lambda_{2} - \lambda_{1}}}{\Phi_{wl} = {\lambda_{w\; 1}\left\lbrack \left( {\frac{\Phi_{{DD\_ L}_{1}}}{\lambda_{1}} - \frac{\Phi_{{DD\_ L}_{2}}}{\lambda_{2}}} \right) \right\rbrack}}\begin{matrix}{C_{\Phi_{wl}} = {{\left( \frac{\lambda_{w\; 1}}{\lambda_{1}} \right)^{2}C_{{{DD\_ L}_{1}{\_ m}},e}} +}} \\{{{\left( \frac{\lambda_{w\; 1}}{\lambda_{2}} \right)^{2}C_{{{DD\_ L}_{2}{\_ m}},e}} + C_{{DD\_ L}_{1}{\_ tropo}} +}} \\{{\left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{2}C_{{{DD\_ L}_{1}{\_ iono}}}}}\end{matrix}{\Phi_{wl\_ flo} = {\Phi_{wl} - {\lambda_{wl}N_{wl\_ flo}}}}{C_{\Phi_{wl\_ flo}} = {C_{\Phi_{wl}} + {\lambda_{wl}^{2}C_{N_{wl\_ flo}}}}}} & (8)\end{matrix}$

WL Fixed :—

Φ_(w1) _(—) _(fix)=Φ_(w1)−λ_(w1) N _(w1) _(—) _(fix)   (9)

C_(Φ) _(w1) _(—) _(fix)=C_(Φ) _(w1)

After the calculations are performed by the first computing module 138,first and second functional modules 139 and 140 select measurement datafor further processing. The best data are selected based on measurementvariance from each of the double difference pair, using theabove-defined methods. The orders are: L1 fixed, L2 fixed, L1 float. L2float, Wide Lane Fixed. Wide Lane Float, and Narrow Lane Code. This wayevery visible satellite is used in the solution, weighted only by itsown relative uncertainty.

A third functional module 141 assembles data for a covariance matrixelement calculation. The covariance matrix to be used in the solution ismore difficult to generate than the other solutions and is done elementby element. Diagonal elements for this solution are simply taken fromthe diagonal elements of the double difference covariance matrix and themeasurement type is determined using the equations above. For examplesif measurement two were a wide land fixed measurement, the M(2, 2)element would be taken from the WL fixed covariance matrix and placed inthe hybrid covariance matrix in the same spot.

A fourth functional module 142 performs the covariance matrix elementcalculation. Off diagonal elements are determined by the relationshipsbetween each measurement type. The simplest way to provide theinformation is to show a complete example and provide the algorithms.For this example the hybrid solution includes each type of measurementin descending order as follows, and each of these measurements is thefirst measurement in its respective solution type.

L1_fixed

L2_fixed

L1_float

L2_float

WL_fixed

WL_float

NL_Code

The covariance matrix is shown by Equation (10):

$\begin{matrix}\begin{bmatrix}{C_{\Phi_{1{\_ fix}}}\left( {1,1} \right)} & a & c & d & e & e & f \\a & {C_{\Phi_{1{\_ fix}}}\left( {1,1} \right)} & h & i & k & k & k \\c & h & {C_{\Phi_{1{\_ fflo}}}\left( {1,1} \right)} & m & n & n & o \\d & i & m & {C_{\Phi_{2{\_ fflo}}}\left( {1,1} \right)} & q & q & r \\e & j & n & q & {C_{\Phi_{WL\_ fix}}\left( {1,1} \right)} & s & t \\e & j & n & q & s & {C_{\Phi_{WL\_ flo}}\left( {1,1} \right)} & t \\f & k & o & r & t & t & {C_{R_{NL}}\left( {1,1} \right)}\end{bmatrix} & (10)\end{matrix}$

where the elements of matrix calculated by Equations (11) to (32:

$\begin{matrix}{a = {\sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{\lambda_{2}^{2}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (11) \\{b = {\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + \sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}} & (12) \\{c = {{\left( {1 - \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}}} \right)*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{\lambda_{2} + {2\lambda_{1}}}{\lambda_{1}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (13) \\{d = {{{- \left( \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}} \right)}*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{{2\lambda_{2}^{2}} + {\lambda_{2}\lambda_{1}}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (14) \\{e = {{\left( \frac{\lambda_{WL}}{\lambda_{1}} \right)*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} - {\left( \frac{\lambda_{2}}{\lambda_{1}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2}}} & (15) \\{f = {\sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} - {\left( \frac{\lambda_{2}}{\lambda_{1}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (16) \\{g = {\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{\lambda_{2}^{4}}{\lambda_{1}^{4}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (17) \\{h = {{\left( \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}} \right)*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{\lambda_{2}^{3} + {2\lambda_{1}\lambda_{2}^{2}}}{\lambda_{1}^{3}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (18) \\{i = {{\left( {1 + \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}}} \right)*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{{2\lambda_{2}^{4}} + {2\lambda_{2}^{3}\lambda_{1}}}{\lambda_{1}^{4}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (19) \\{j = {{{- \left( \frac{\lambda_{WL}}{\lambda_{2}} \right)}*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} - {\left( \frac{\lambda_{2}^{3}}{\lambda_{1}^{3}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2}}} & (20) \\{k = {\sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} - {\left( \frac{\lambda_{2}^{3}}{\lambda_{1}^{3}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (21) \\{l = {{\left( {1 - \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}}} \right)^{2}*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + {\left( \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}} \right)^{2}*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{{2\lambda_{1}} + \lambda_{2}}{\lambda_{1}} \right)^{2}*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (22) \\{m = {{{- \left( {1 - \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}}} \right)}\left( \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}} \right)*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( {1 + \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}}} \right)\left( \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}} \right)*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + {\left( \frac{{2\lambda_{2}^{3}} + {5\lambda_{2}^{2}\lambda_{1}} + {2\lambda_{1}^{2}\lambda_{2}}}{\lambda_{1}^{3}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (23) \\{n = {{{- \left( \frac{\lambda_{WL}}{\lambda_{2}} \right)}*\left( \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}} \right)*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + {\left( \frac{\lambda_{WL}}{\lambda_{2}} \right)*\left( {1 - \frac{\lambda_{1}}{\lambda_{2} - \lambda_{1}}} \right)*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} - {\left( \frac{{2\lambda_{1}\lambda_{2}} + \lambda_{2}^{2}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (24) \\{o = {\sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} - {\left( \frac{{2\lambda_{1}\lambda_{2}} + \lambda_{2}^{2}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (25) \\{p = {{\left( \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}} \right)^{2}*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + {\left( {1 + \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}}} \right)^{2}*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{{2\lambda_{2}^{2}} + {\lambda_{2}\lambda_{1}}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (26) \\{q = {{{- \left( \frac{\lambda_{WL}}{\lambda_{1}} \right)}*\left( \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}} \right)*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} - {\left( \frac{\lambda_{WL}}{\lambda_{2}} \right)*\left( {1 + \frac{\lambda_{2}}{\lambda_{2} - \lambda_{1}}} \right)*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} - {\left( \frac{{2\lambda_{2}^{3}} + {\lambda_{2}^{2}\lambda_{1}}}{\lambda_{1}^{3}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (27) \\{r = {\sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} - {\left( \frac{{2\lambda_{2}^{3}} + {\lambda_{2}^{2}\lambda_{1}}}{\lambda_{1}^{3}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (28) \\{s = {{\left( \frac{\lambda_{WL}}{\lambda_{2}} \right)^{2}*\sigma_{{{AB\_ L}\; 2{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + {\left( \frac{\lambda_{WL}}{\lambda_{1}} \right)^{2}*\sigma_{{{AB\_ L}\; 1{\_ m}},{{e\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{\lambda_{2}^{2}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (29) \\{t = {{\left( \frac{\lambda_{2}^{2}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2}}} & (30) \\{u = {s + {\lambda_{WL}^{2}*C_{{mw\_ SD}{\_ fl}{\_ key}}}}} & (31) \\{v = {{\left( \frac{\lambda_{NL}}{\lambda_{1}} \right)^{2}*\sigma_{{{AB\_ L}\; 1{\_ M}},{{E\_ key}{\_ SV}}}^{2}} + {\left( \frac{\lambda_{NL}}{\lambda_{2}} \right)^{2}*\sigma_{{{AB\_ L}\; 2{\_ M}},{{E\_ key}{\_ SV}}}^{2}} + \sigma_{{AB\_ tropo}{\_ key}{\_ sv}}^{2} + {\left( \frac{\lambda_{2}^{2}}{\lambda_{1}^{2}} \right)*\sigma_{{AB\_ L}\; 1{\_ iono}{\_ key}{\_ sv}}^{2}}}} & (32)\end{matrix}$

The cases not covered in the example are the relationships betweencommon solutions. In these cases the following applies:

L1_fixed to L1_fixed is equivalent to b;

L2_fixed to L2_fixed is equivalent to g;

L1_float to L1_float is equivalent to l;

L2 float to L2_float is equivalent top;

WL_fixed to WL fixed is equivalent to s;

WL_float to WL_float is equivalent to u; and

NL code to NL code is equivalent to v:

A fifth functional module 143 calculates a Relative Position Solutionusing the Weighted Least Squares Method. The measurements should includeevery satellite, using the most accurate (smallest variance) measurementavailable for that satellite. The calculations executed by differentsteps of the WLS algorithm are shown below. The initialization isperformed once at the start of a filter. All other steps are iterated (2or 3 times) until a solution converges.

Step 1 initializes the baseline vector b (at start of the filter) byEquation (33)

x_(k) ⁻=0   (33)

Step 2 calculates Measurements and Covariance by Equations (34), (35)and (36):

Z=Z_(Hybrid)   (34)

C_(z)=Σ_(Hybrid)   (35)

W=C_(z) ⁻¹   (36)

Step 3 calculates LOS (Line of Sight) vectors from Ship and Aircraft toSatellite j by Equations (37)-(42):

In the equations, satellite position {x^(s),y^(s),z^(s)} is fromephemeris and ship position {x_(A),y_(A),z_(A)} is from an absoluteposition solution. LOS Vectors:

$\begin{matrix}\begin{matrix}{{Ship}\mspace{11mu} (A)\mspace{11mu} {to}\mspace{14mu} {satellite}\mspace{14mu} j} & {{{as}(j)} = \begin{bmatrix}{{x^{s}(j)} - x_{A}} \\{{y^{s}(j)} - y_{A}} \\{{z^{s}(j)} - z_{A}}\end{bmatrix}} \\{{Aircraft}\mspace{11mu} (B)\mspace{11mu} {to}\mspace{14mu} {satellite}\mspace{14mu} j} & \begin{matrix}{{{bs}(j)} = \begin{bmatrix}{{x^{s}(j)} - x_{B}} \\{{y^{s}(j)} - y_{B}} \\{{z^{s}(j)} - z_{B}}\end{bmatrix}} \\{= \begin{bmatrix}{{x^{s}(j)} - \left( {x_{A} + {\hat{b}}_{x}} \right)} \\{{y^{s}(j)} - \left( {y_{A} + {\hat{b}}_{y}} \right)} \\{{z^{s}(j)} - \left( {z_{A} + {\hat{b}}_{z}} \right)}\end{bmatrix}}\end{matrix}\end{matrix} & \begin{matrix}(37) \\\; \\\; \\\; \\(38)\end{matrix}\end{matrix}$

Magnitudes of LOS vectors:

as_mag(j)=∥as(j)∥;and   (39)

bs_mag(j)=∥bs(j)∥  (40)

Predicted SD Measurement (as-bs)

dab(j)=as_mag(j)−bs_mag(j);   (41)

Predicted DD Measurements

$\begin{matrix}{Z_{k}^{-} = \begin{bmatrix}{{{dab}(1)} - {{dab}(2)}} \\{{{dab}(1)} - {{dab}(3)}} \\\ldots \\{{{dab}(1)} - {{dab}(K)}}\end{bmatrix}} & (42)\end{matrix}$

using satellite 1 (highest) as reference

Step 4 performs Linearization by evaluating Equations (43)-(45):

Unit LOS Vectors from Aircraft to Satellite j:

$\begin{matrix}{\begin{bmatrix}{1_{x}(j)} \\{1_{y}(j)} \\{1_{z}(j)}\end{bmatrix} = {{{{bs}(j)}/{bs\_ mag}}(j)}} & (43)\end{matrix}$

Differences of Unit Vectors

e _(x)(1,j)=1_(x)(1)−1_(x)(j)

e _(y)(1,j)=1_(y)(1)−1_(y)(j)   (44)

e _(z)(1,j)=1_(z)(1)−1_(z)(j)

H Matrix (Matrix Formed by Differenced Unit Vectors)

$\begin{matrix}{H = \begin{bmatrix}{e_{x}\left( {1,2} \right)} & {e_{y}\left( {1,2} \right)} & {e_{z}\left( {1,2} \right)} \\{e_{x}\left( {1,3} \right)} & {e_{y}\left( {1,3} \right)} & {e_{z}\left( {1,3} \right)} \\\cdots & \cdots & \cdots \\\cdots & \cdots & \cdots \\\cdots & \cdots & \cdots\end{bmatrix}} & (45)\end{matrix}$

Steps 5 computes the Weighted Least Square Relative Position solution byEquations (46)-(49):

Filter Observable:

ΔZ=[Z _(k) −Z _(k) ⁻]  (46)

WLS Solution and Solution Covariance:

Δ{circumflex over (x)}=[H^(T)WH]⁻¹H^(T)W ΔZ   (47)

{circumflex over (x)} _(k) ⁺ ={circumflex over (x)} _(k) ⁻ +Δ{circumflexover (x)}  (48)

Σ_({circumflex over (x)})=[H^(T)W H]⁻¹   (49)

The solution is arrived at by transforming each Relative PositionSolution and its Covariance from WGS-84 to NED coordinates(north-east-down coordinates at ship reference point).

The final output from the process includes the following data:

Hybrid Relative Position NED

Covariance of Hybrid Relative Position

1. A method of calculating position data for an airborne aircraft usinga GPS-based airborne navigation system, comprising processing a positioncomponent of a relative state function by fusing a plurality ofdifferent types of measurement data axailable in the GPS-based systeminto a weighted least squares algorithm to determine an appropriatecovariance matrix for the plurality of different types of measurementdata.
 2. A method for calculating position. velocity, and accelerationdata for an airborne craft using a GPS based navigation system.comprising: processing position. velocity, and acceleration componentsof a relative state function by fusing a plurality of measurement datatypes into a weighted least squares algorithm; and determining anappropriate covariance matrix for the plurality of measurement datatypes, wherein errors in the position, velocity and acceleration dataare minimized.
 3. The method of claim
 2. wherein at least one of themeasurement data pes is measured for a ship.
 4. The method of claim 2,wherein at least one of the measurement data types is measured for anairborne aircraft.
 5. The method of claim 2, wherein at least one of themeasurement data types is measured for a stationary geographic point. 6.The method of claim 2, wherein the processing includes the calculationof wide lane phase ambiguities.
 7. The method of claim 2, wherein theairborne craft position, velocity and acceleration data are combinedwith a ships position, velocity and acceleration data to produce arelative vector solution between the airborne craft and the ship.
 8. Themethod of claim 7, wherein the processing includes the determination ofthe quality of the relative vector solution between the airborne craftand the ship.
 9. An apparatus for calculating position velocity andacceleration data for an airborne aircraft using a GPS based navigationsystem, comprising: a data acquisition device operable to acquire aplurality of measured position, velocity and acceleration data typesusing the GPS based navigation system; and a calculating device operableto fuse the plurality of measured data types in a weighted least squaresalgorithm, whereby an appropriate covariance matrix is determined forthe plurality of data types such that errors in the position, velocityand acceleration data are minimized.
 10. The apparatus of claim 9,wherein at least one of the data types is acquired from the aircraft andat least one of data types is acquired from a reference locationselected from the group consisting of a ship and a stationary geographicpoint.
 11. The apparatus of claim 9, wherein the calculating device isfurther operable to calculate wide lane phase ambiguities.
 12. Theapparatus of claim 9, wherein the calculating device is further operableto combine the aircraft's position, velocity, and acceleration data anda ship's position, velocity and acceleration data to produce a relativevector solution between the airborne craft and the ship.
 13. Theapparatus of claim 12, wherein the calculating device is furtheroperable to determine the quality of the relative vector solutionbetween the aircraft and the ship.
 14. An airborne navigation system forcalculating position, velocity and acceleration data for an airborneaircraft using a GPS based navigation system, comprising: a plurality ofGPS data acquisition devices operable to determine a plurality ofposition, velocity and acceleration data types of a ship and theairborne aircraft; and a calculating component operable to fuse theplurality of data types in a weighted least squares algorithm, so as todetermine an appropriate covariance matrix for the plurality of datatype such that errors in the position, velocity and acceleration dataare minimized.
 15. The system of claim 14, wherein at least one of thedata types is measured for the aircraft, and at least one of the datatypes is measured from a reference location selected from the groupconsisting of a ship and a fixed geographic location.
 16. The system ofclaim 14, wherein the calculating component is further operable tocalculate wide lane phase ambiguities.
 17. The system of claim 14,wherein the calculating component is further operable to combineairborne aircraft position, velocity and acceleration data with a ship'sposition, velocity and acceleration data to produce a relative vectorsolution between the airborne aircraft and the ship.
 18. The system ofclaim 17, wherein the calculating component is further operable todetermine the quality of the relative vector solution between theairborne aircraft and the ship.
 19. A method of calculating positiondata of a moving craft by fusing different types of measurement data,comprising: transmitting Global Positioning System (GPS) measurementdata from a GPS satellite constellation to the moving craft: computingposition. velocity, and estimated wide lane phase ambiguity data by areference location employing a weighted least squares algorithm:transmitting the computed data from the reference location to the movingcraft; and combining the measurement data and the computed data by themoving craft to produce a relative vector solution between its ownlocation and the reference location.
 20. The method of claim 19, whereinthe moving craft is an airborne aircraft.
 21. The method of claim 19,wherein the reference location is a ship.
 22. A method of calculating arelative position and a velocity vector between a ship and an airborneaircraft and providing this information as basic relative state (BRS)data and precision relative state (PRS) data to the aircraft byemploying a weighted least squares algorithm, the method comprising:calculating Double-Difference measurements at a ship time: determiningWide Lane Float Ambiguities and a covariance value; determining firstand second frequency float ambiguities and a covariance calculation fromthe Double-Difference measurements, the Wide Lane Float Ambiguities. andthe covariance value; calculating a PRS solution of the aircraft fromthe first and second frequency float ambiguities and the covariancecalculation: computing a BRS solution and a BRS covariance value at anaircraft time; and transmitting the BRS and PRS solutions to theaircraft.
 23. A method of calculating a Precision Relative State (PRS)solution for an airborne navigation system by processing a plurality ofdifferent types of measurement data, comprising: computing code rangeand phase range values from measurements and variances from satellitedata; selecting measurement data values having the smallest variancefrom the computed code range and phase range values: assembling theselected data for a covariance matrix elements calculation; building thecovariance matrix by calculating values for its elements; andcalculating the PRS solution and its covariance using the covariancematrix by a weighted least squares (WLS) algorithm
 24. The method ofclaim 23, wherein the step of calculating the PRS solution and itscovariance includes repeating the calculation until the PRS solutionconverges.
 25. The method of claim 23, wherein the satellite datainclude data from at least two Global Positioning System (GPS)satellites.
 26. A landing system for an airborne aircraft, comprising: areference location having means for computing and transmitting referencelocation position, velocity, and estimated wide lane phase ambiguitydata using a weighted least squares algorithm: a GPS satelliteconstellation operable to transmit GPS measurement data: a receiver onthe moving craft that is operable to receive the measurement data fromthe GPS satellite constellation and the computed data from the referencelocation: and a calculating system associated with the receiver that isoperable to calculate position data for the aircraft by ftising themeasurement data and the reference data with a weighted least squares(WLS) algorithm.
 27. The landing system of claim 6, wherein the aircrafthas a navigation system operable to combine measurement data andcomputed data for producing a relati e vector solution between its ownlocation and the reference location.
 28. The landing system of claim 26,wherein the eference location is a ship having a Relative Navigation(RelNav) system operable to calculate a relative position and a velocityvector between the ship and the aircraft.
 29. The landing system ofclaim 28, wherein the relative position and a velocity vector aretransmitted to the aircraft by the ship.
 30. An Airborne RelativeNavigation (RelNav) system for calculating a relative position and avelocity vector between a ship and an airborne aircraft and forproviding this information as relative state to the aircraft,comprising: a Measurement Management and Validation function thatprocesses and validates incoming measurement data; a RelativeMeasurements function that calculates Double-Difference measurements andvariance components from Single-Difference measurements; a Wide LaneAmbiguities function that determines wide lane float ambiguities and afirst covariance value; an ambiguities function that determines firstand second frequency float ambiguities and a second covariance value;and a relative state function that computes a relative state andcovariance solution from the wide lane float ambiguities, the firstcovariance value, the firs and second frequency float ambiguities andthe second covariance alue. and that provides the solution to an avionicsystem on the aircraft using a weighted least squares algorithm.
 31. TheRelNav system of claim 30, wherein the covariance values includecorrections for at least one of: multi-path, noise, ionosphere, ortroposphere errors.
 32. The RelNav system of claim 20, wherein thecovariance values are selected from the group consisting of at least oneof multi-path, noise, ionosphere corrections, and tropospherecorrections.
 33. A Precision Relative State (PRS) computational modulefor calculating a PRS solution for an airborne navigation system,employing a weighted least squares (WLS) algorithm for processing aplurality of different types of measurement data, comprising: an inputcomputing module operable to compute code range and phase range valuesfrom measurement and covariance data from a satellite; a data selectionmodule operable to select data based on measurement variances; acovariance matrix-building module operable to assemble data for acovariance matrix element calculation; a covariance matrix elementcalculation module for determining values for the covariance matrixelements; and a PRS solution calculation module operable to calculatethe PRS solution and its covariance using the covariance matrix by theWLS algorithm.
 34. The PRS computational module of claim 33, wherein theinput computing module includes measurement data from exery availableGlobal Positioning System (GPS) satellite.
 35. The PRS computationalmodule of claim 33, wherein the WLS algorithm includes: an operation forcalculating measurements and covariance; an operation for calculatingLine of Sight (LOS) vectors from a ship and an aircraft to a satellite;an operation for performing linearization of LOS vectors; an operationfor calculating WLS of relative position solutions; and an operation fortransforming each relative position solution and its covariance fromWorld Geodetic System of 1984 coordinates to North-East-Down coordinatesat a ship reference point.
 36. The PRS computational module of claim 33,wherein the relative position solution calculation module operatesiteratively until the PRS solution converges.